Suggested citation: > Miranti, Ragdad Cani.(2020). Regional Poverty Convergence across Districts in Indonesia: A Distribution Dynamics Approach https://rpubs.com/canimiranti/distribution_dynamics_poverty514districts
This work is licensed under the Creative Commons Attribution-Non Commercial-Share Alike 4.0 International License.
Original data source
Data of Headcount Index (Poverty Rate) are derived from the Indonesia Central Bureau of Statistics (Badan Pusat Statistik Republik of Indonesia). https://www.bps.go.id/
Acknowledgment:
Material adapted from multiple sources, in particular from Magrini (2007).
Libraries
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(skimr)
library(kableExtra) # html tables
library(pdfCluster) # density based clusters
library(hdrcde) # conditional density estimation
library(plotly)
library(intoo)
library(barsurf)
library(bivariate)
library(np)
library(quantreg)
library(basetheme)
basetheme("minimal")
library(viridis)
library(ggpointdensity)
library(isoband)
#library(MASS)
library(KernSmooth)
# Change the presentation of decimal numbers to 4 and avoid scientific notation
options(prompt="R> ", digits=4, scipen=7)
Tutorial objectives
Study the dynamics of univariate densities
Compute the bandwidth of a density
Study mobility plots
Study bi-variate densities
Study density-based clustering methods
Study conditional bi-variate densities
Import data
dat <- read_csv("poverty.csv")
dat <- as.data.frame(dat)
Descriptive statistics
── Data Summary ────────────────────────
Values
Name dat
Number of rows 514
Number of columns 13
_______________________
Column type frequency:
character 1
numeric 12
________________________
Group variables None
── Variable type: character ────────────────────────────────────────────────────────────
skim_variable n_missing complete_rate min max empty n_unique whitespace
1 District 0 1 4 26 0 514 0
── Variable type: numeric ──────────────────────────────────────────────────────────────
skim_variable n_missing complete_rate mean sd p0 p25 p50
1 Code 0 1 4558. 2678. 911 1803. 3550
2 pov2010 0 1 15.6 9.42 1.67 9.01 13.3
3 pov2011 0 1 14.6 8.92 1.5 8.14 12.4
4 pov2012 0 1 13.9 8.55 1.33 7.79 11.8
5 pov2013 0 1 13.8 8.59 1.75 7.76 11.7
6 pov2014 0 1 13.1 7.93 1.68 7.38 11.2
7 pov2015 0 1 13.5 8.25 1.69 7.59 11.6
8 pov2016 0 1 13.2 8.20 1.67 7.40 11.2
9 pov2017 0 1 13.0 7.98 1.76 7.35 11.1
10 pov2018 0 1 12.3 7.84 1.68 6.99 10.2
11 rel_pov2010 0 1 1 0.603 0.107 0.577 0.854
12 rel_pov2018 0 1 1.27 0.763 0.135 0.730 1.08
p75 p100 hist
1 7174. 9471 ▇▆▂▇▃
2 19.6 49.6 ▇▇▂▁▁
3 18.9 47.4 ▇▇▂▁▁
4 17.8 45.9 ▇▇▂▁▁
5 17.4 47.5 ▇▆▂▁▁
6 16.6 44.5 ▇▆▂▁▁
7 16.9 45.7 ▇▇▂▁▁
8 16.3 45.1 ▇▇▂▁▁
9 16.0 43.6 ▇▇▂▁▁
10 15.1 43.5 ▇▆▂▁▁
11 1.25 3.18 ▇▇▂▁▁
12 1.59 4.02 ▇▇▂▁▁
xy <- dat %>%
select(
pov2010,
pov2018,
) %>%
mutate(
x = pov2010,
y = pov2018
) %>%
select(
x,
y
)
Univariate dynamics
Select bandwiths
Select bandwidth based on function dpik from the package KernSmooth
h_rel_pov2010<- dpik(dat$rel_pov2010)
h_rel_pov2010
[1] 0.1026
h_rel_pov2018 <- dpik(dat$rel_pov2018)
h_rel_pov2018
[1] 0.1299
Plot each density
dis_rel_pov2010 <- bkde(dat$rel_pov2010, bandwidth = h_rel_pov2010)
dis_rel_pov2010 <- as.data.frame(dis_rel_pov2010)
ggplot(dis_rel_pov2010, aes(x, y)) + geom_line() +
theme_minimal()

dis_rel_pov2018 <- bkde(dat$rel_pov2018, bandwidth = h_rel_pov2018)
dis_rel_pov2018 <- as.data.frame(dis_rel_pov2018)
ggplot(dis_rel_pov2018, aes(x, y)) + geom_line() +
theme_minimal()

Plot both densities
There are two methods for plot both densities,i.e. Kernsmooth and bandwith default of ggplot. I prefer using the gglot ( Method 2).
Method 2 (ggplot)
Using the bandwidth default of ggplot Manual labels are not yet implemented in the ggplotly function
rel_pov2010 <- dat %>%
select(rel_pov2010) %>%
rename(rel_var = rel_pov2010) %>%
mutate(year = 2010)
rel_pov2018 <- dat %>%
select(rel_pov2018) %>%
rename(rel_var = rel_pov2018) %>%
mutate(year = 2018)
rel_pov2010pov2018 <- bind_rows(rel_pov2010, rel_pov2018)
rel_pov2010pov2018 <- rel_pov2010pov2018 %>%
mutate(year = as.factor(year))
head(rel_pov2010pov2018)
dis_rel_pov2010pov2018 <- ggplot(rel_pov2010pov2018,aes(x=rel_var, color=year)) +
geom_density() +
theme_minimal()
dis_rel_pov2010pov2018

Using plotly
ggplotly(dis_rel_pov2010pov2018)
Bivariate density
Using Mobility scatterplot
dat %>%
ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
geom_point(alpha=0.5) +
geom_abline(aes(intercept = 0, slope = 1)) +
geom_hline(yintercept = 1, linetype="dashed") +
geom_vline(xintercept = 1, linetype="dashed") +
theme_minimal() +
labs(subtitle = "Relative Pov2018",
x = "Relative Pov2010",
y = "") +
theme(text=element_text(family="Palatino"))

Fit a non-linear function
dat %>%
ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
geom_point(alpha=0.5) +
geom_smooth() +
geom_abline(aes(intercept = 0, slope = 1)) +
geom_hline(yintercept = 1, linetype="dashed") +
geom_vline(xintercept = 1, linetype="dashed") +
theme_minimal() +
labs(subtitle = "Relative pov2018",
x = "Relative pov2010",
y = "") +
theme(text=element_text(family="Palatino"))

Not that the nonlinear fit crosses the 45-degree line two times from above.
Using the Bivariate package
bivariate <- kbvpdf(dat$rel_pov2010, dat$rel_pov2018, h_rel_pov2010, h_rel_pov2018)
plot(bivariate,
xlab="Relative Poverty 2010",
ylab="Relative Poverty 2018")
abline(a=0, b=1)

plot(bivariate,
TRUE,
xlab="Relative Poverty 2010",
ylab="Relative Poverty 2018")

Using ggplot (stat_density_2d)
dat %>%
ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
geom_point(color = "lightgray") +
geom_smooth() +
#geom_smooth(method=lm, se=FALSE) +
stat_density_2d() +
geom_abline(aes(intercept = 0, slope = 1)) +
geom_hline(yintercept = 1, linetype="dashed") +
geom_vline(xintercept = 1, linetype="dashed") +
theme_minimal() +
labs(subtitle = "Relative pov2018",
x = "Relative pov2010",
y = "") +
theme(text=element_text(family="Palatino"))

dat %>%
ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
stat_density_2d(aes(fill = stat(nlevel)), geom = "polygon") +
scale_fill_viridis_c() +
geom_abline(aes(intercept = 0, slope = 1)) +
geom_hline(yintercept = 1, linetype="dashed") +
geom_vline(xintercept = 1, linetype="dashed") +
theme_minimal() +
labs(x = "Relative Poverty Rate 2010",
y = "Relative Poverty Rate 2018") +
theme(text=element_text(size=8, family="Palatino"))

Using Stochastic Kernel Package
There are two ways of analyzing the use of stochastic kernel package: 1. Contour Plots and 2. Surface Plots
Contour Plots
pov2010pov2018 <- cbind(dat$rel_pov2010, dat$rel_pov2018)
pov2010pov2018_dis <- bkde2D(pov2010pov2018, bandwidth = c(h_rel_pov2010, h_rel_pov2018))
contour(pov2010pov2018_dis$x1,pov2010pov2018_dis$x2,pov2010pov2018_dis$fhat)
abline(a=0, b=1)

Surface Plots
plot_ly(x=pov2010pov2018_dis$x1, y=pov2010pov2018_dis$x2, z=pov2010pov2018_dis$fhat) %>% add_surface()
plot_ly(x=pov2010pov2018_dis$x1, y=pov2010pov2018_dis$x2, z=pov2010pov2018_dis$fhat, type = "contour", contours = list(showlabels = TRUE)) %>%
colorbar(title = "Density")
Conditional density analysis
Using the hdrcde package
pov2010pov2018_cde <- cde(dat$pov2010, dat$pov2018)
Increase the number of intervals to 20
pov2010pov2018_cde2 <- cde(dat$pov2010, dat$pov2018, nxmargin = 20)

plot(pov2010pov2018_cde2)

High density regions
plot(pov2010pov2018_cde, plot.fn="hdr")
abline(a=0, b=1)

References
Magrini, S. (2007). Analysing convergence through the distribution dynamics approach: why and how?. University Ca’Foscari of Venice, Dept. of Economics Research Paper Series No, 13.
Mendez C. (2020). Classical sigma and beta convergence analysis in R: Using the REAT 2.1 Package. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/classical-convergence-reat21
Mendez C. (2020). Univariate distribution dynamics in R: Using the ggridges package. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/univariate-distribution-dynamics
Mendez, C. (2020) Regional efficiency convergence and efficiency clusters. Asia-Pacific Journal of Regional Science, 1-21.
Mendez, C. (2019). Lack of Global Convergence and the Formation of Multiple Welfare Clubs across Countries: An Unsupervised Machine Learning Approach. Economies, 7(3), 74.
Mendez, C. (2019). Overall efficiency, pure technical efficiency, and scale efficiency across provinces in Indonesia 1990 and 2010. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/efficiency-clusters-indonesia-1990-2010
Mendez-Guerra, C. (2018). On the distribution dynamics of human development: Evidence from the metropolitan regions of Bolivia’’. Economics Bulletin, 38(4), 2467-2475.
END
---
title: "Regional Poverty Convergence across Districts in Indonesia:A Distribution Dynamics Approach"
author: "Ragdad Cani Miranti"
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Suggested citation: 
> Miranti, Ragdad Cani.(2020). Regional Poverty Convergence across Districts in Indonesia: A Distribution Dynamics Approach <https://rpubs.com/canimiranti/distribution_dynamics_poverty514districts>


This work is licensed under the Creative Commons Attribution-Non Commercial-Share Alike 4.0 International License. 

# Original data source

Data of Headcount Index (Poverty Rate) are derived from the Indonesia Central Bureau of Statistics (Badan Pusat Statistik Republik of Indonesia). <https://www.bps.go.id/>

Acknowledgment:

Material adapted from multiple sources, in particular from [Magrini (2007).](https://pdfs.semanticscholar.org/eab1/cb89dde0c909898b0a43273377c5dfa73ebc.pdf)

# Libraries

```{r message=FALSE, warning=FALSE}
knitr::opts_chunk$set(echo = TRUE)

library(tidyverse)
library(skimr)
library(kableExtra)    # html tables 
library(pdfCluster)    # density based clusters
library(hdrcde)        # conditional density estimation 
library(plotly)

library(intoo)
library(barsurf)
library(bivariate)

library(np)
library(quantreg)

library(basetheme)
basetheme("minimal")

library(viridis)
library(ggpointdensity)
library(isoband)

#library(MASS)
library(KernSmooth)


# Change the presentation of decimal numbers to 4 and avoid scientific notation
options(prompt="R> ", digits=4, scipen=7)

```

# Tutorial objectives

- Study the dynamics of univariate densities

- Compute the bandwidth of a density

- Study mobility plots

- Study bi-variate densities

- Study density-based clustering methods

- Study conditional bi-variate densities



# Import data

```{r message=FALSE, warning=TRUE}
dat <- read_csv("poverty.csv")
dat <- as.data.frame(dat)
```


# Transform data


Since the data is in relative terms, let us rename the variables and add new variables.


```{r}
dat <- dat %>% 
  mutate(
    rel_pov2010 = pov2010/mean(pov2010),
    rel_pov2018 = pov2010/mean(pov2018)
  )
dat
```



# Descriptive statistics

```{r}
skim(dat)
```


```{r}
xy <- dat %>% 
select(
pov2010,
pov2018,
  ) %>% 
  mutate(
    x = pov2010,
    y = pov2018
  ) %>% 
  select(
    x,
    y
  )

```


# Univariate dynamics

## Select bandwiths

Select bandwidth based on function `dpik` from the package `KernSmooth`

```{r}
h_rel_pov2010<- dpik(dat$rel_pov2010)
h_rel_pov2010
```


```{r}
h_rel_pov2018 <- dpik(dat$rel_pov2018)
h_rel_pov2018
```

## Plot each density

```{r}
dis_rel_pov2010 <- bkde(dat$rel_pov2010, bandwidth = h_rel_pov2010)
dis_rel_pov2010 <- as.data.frame(dis_rel_pov2010)
ggplot(dis_rel_pov2010, aes(x, y)) + geom_line() + 
  theme_minimal() 
```


```{r}
dis_rel_pov2018 <- bkde(dat$rel_pov2018, bandwidth = h_rel_pov2018)
dis_rel_pov2018 <- as.data.frame(dis_rel_pov2018)
ggplot(dis_rel_pov2018, aes(x, y)) + geom_line() + 
  theme_minimal() 
```


## Plot both densities

There are two methods for plot both densities,i.e. Kernsmooth and bandwith default of ggplot. I prefer using the gglot ( Method 2).

# Method 2 (ggplot)

Using the bandwidth default of ggplot 
Manual labels are not yet implemented in the `ggplotly` function

```{r}
rel_pov2010 <- dat %>% 
  select(rel_pov2010) %>% 
  rename(rel_var = rel_pov2010) %>% 
  mutate(year = 2010)
```

```{r}
rel_pov2018 <- dat %>% 
  select(rel_pov2018) %>% 
  rename(rel_var = rel_pov2018) %>% 
  mutate(year = 2018)
```

```{r}
rel_pov2010pov2018 <- bind_rows(rel_pov2010, rel_pov2018)
```
 
```{r}
rel_pov2010pov2018 <- rel_pov2010pov2018 %>% 
  mutate(year = as.factor(year))
head(rel_pov2010pov2018)
```
 
 

```{r}
dis_rel_pov2010pov2018 <- ggplot(rel_pov2010pov2018,aes(x=rel_var, color=year)) +
  geom_density() + 
  theme_minimal() 
dis_rel_pov2010pov2018
```


Using plotly

```{r}
ggplotly(dis_rel_pov2010pov2018)
```



# Bivariate density

## Using Mobility scatterplot

```{r}
dat %>% 
  ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
  geom_point(alpha=0.5) +
  geom_abline(aes(intercept = 0, slope = 1)) +
  geom_hline(yintercept = 1, linetype="dashed") + 
  geom_vline(xintercept = 1, linetype="dashed") +
  theme_minimal() +
  labs(subtitle = "Relative Pov2018",
       x = "Relative Pov2010",
       y = "") +
  theme(text=element_text(family="Palatino")) 
```


Fit a non-linear function

```{r}
dat %>% 
  ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
  geom_point(alpha=0.5) + 
  geom_smooth() + 
  geom_abline(aes(intercept = 0, slope = 1)) +
  geom_hline(yintercept = 1, linetype="dashed") + 
  geom_vline(xintercept = 1, linetype="dashed") +
  theme_minimal() +
  labs(subtitle = "Relative pov2018",
       x = "Relative pov2010",
       y = "") +
  theme(text=element_text(family="Palatino")) 
```

Not that the nonlinear fit crosses the 45-degree line two times from above.

## Using the Bivariate package

```{r}
bivariate <- kbvpdf(dat$rel_pov2010, dat$rel_pov2018, h_rel_pov2010, h_rel_pov2018) 
```


```{r}
plot(bivariate,
      xlab="Relative Poverty 2010", 
      ylab="Relative Poverty 2018")
abline(a=0, b=1)
abline(h=1, v=1)
```


```{r}
plot(bivariate,
      TRUE,
      xlab="Relative Poverty 2010", 
      ylab="Relative Poverty 2018")
```


## Using ggplot (stat_density_2d)

```{r}
dat %>% 
  ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
  geom_point(color = "lightgray") + 
  geom_smooth() + 
  #geom_smooth(method=lm, se=FALSE) + 
  stat_density_2d() +
  geom_abline(aes(intercept = 0, slope = 1)) +
  geom_hline(yintercept = 1, linetype="dashed") + 
  geom_vline(xintercept = 1, linetype="dashed") +
  theme_minimal() +
  labs(subtitle = "Relative pov2018",
       x = "Relative pov2010",
       y = "") +
  theme(text=element_text(family="Palatino")) 
```



```{r}
dat %>% 
  ggplot(aes(x = rel_pov2010, y = rel_pov2018)) +
        stat_density_2d(aes(fill = stat(nlevel)), geom = "polygon") + 
  scale_fill_viridis_c() +
        geom_abline(aes(intercept = 0, slope = 1)) +
        geom_hline(yintercept = 1, linetype="dashed") + 
        geom_vline(xintercept = 1, linetype="dashed") + 
  theme_minimal() +
        labs(x = "Relative Poverty Rate 2010",
             y = "Relative Poverty Rate 2018") +
        theme(text=element_text(size=8, family="Palatino"))
```


## Using Stochastic Kernel Package

There are two ways of analyzing the use of stochastic kernel package: 1. Contour Plots
and 2. Surface Plots

### Contour Plots

```{r}
pov2010pov2018 <- cbind(dat$rel_pov2010, dat$rel_pov2018)
pov2010pov2018_dis <- bkde2D(pov2010pov2018, bandwidth = c(h_rel_pov2010, h_rel_pov2018)) 
```

```{r}
contour(pov2010pov2018_dis$x1,pov2010pov2018_dis$x2,pov2010pov2018_dis$fhat)
abline(a=0, b=1)
```

### Surface Plots

```{r}
plot_ly(x=pov2010pov2018_dis$x1, y=pov2010pov2018_dis$x2, z=pov2010pov2018_dis$fhat) %>% add_surface()
```
```{r}
plot_ly(x=pov2010pov2018_dis$x1, y=pov2010pov2018_dis$x2, z=pov2010pov2018_dis$fhat, type = "contour", contours = list(showlabels = TRUE))  %>%
  colorbar(title = "Density")
```

# Conditional density analysis

## Using the `hdrcde` package

```{r}
pov2010pov2018_cde <- cde(dat$pov2010, dat$pov2018)
```

Increase the number of intervals to 20

```{r}
pov2010pov2018_cde2 <- cde(dat$pov2010, dat$pov2018, nxmargin = 20)
```


```{r}
plot(pov2010pov2018_cde)
```


```{r}
plot(pov2010pov2018_cde2)
```


High density regions


```{r}
plot(pov2010pov2018_cde, plot.fn="hdr")
abline(a=0, b=1)
abline(h=1, v=1)
```


# References

- [Magrini, S. (2007). Analysing convergence through the distribution dynamics approach: why and how?. University Ca'Foscari of Venice, Dept. of Economics Research Paper Series No, 13. ](https://pdfs.semanticscholar.org/eab1/cb89dde0c909898b0a43273377c5dfa73ebc.pdf)

- Mendez C. (2020). Classical sigma and beta convergence analysis in R: Using the REAT 2.1 Package. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/classical-convergence-reat21

- Mendez C. (2020). Univariate distribution dynamics in R: Using the ggridges package. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/univariate-distribution-dynamics

- [Mendez, C. (2020) Regional efficiency convergence and efficiency clusters. Asia-Pacific Journal of Regional Science, 1-21.](http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8YThSI5bKW06znW3BanO-2FRs-3D_u6a2PqF3vslNNtSRbhxJPcJKxO5EKzOsf0-2FWiizN57d4csF7ReMur5e40TbX48DbSe9kEMCwFpvvFpLcuaVB-2BpdC3fLCbsP0iKcsxIs1dv1yrPsGDCNh5bhgvI8-2F-2Bxwz7upjDgycqPbhObNqkT41uqY3dPiXr5vBoY1xwT88MA3-2FbdJgwoBl1Gnzli13mkmlJj0kqTs-2BllVfCTB356mLjjKR2VBZCUgKbyVpYgu1vXjwTwdOyzd5FTbU8eaRsWyORje7WCPpGEKCUAvbeTCSPa2rfdkmnkQIrsmYBSqfSZ8aaWzHwIkMU3hxbIU6nHGQ) 

- [Mendez, C. (2019). Lack of Global Convergence and the Formation of Multiple Welfare Clubs across Countries: An Unsupervised Machine Learning Approach. Economies, 7(3), 74.](https://www.mdpi.com/2227-7099/7/3/74/pdf)

- Mendez, C. (2019). Overall efficiency, pure technical efficiency, and scale efficiency across provinces in Indonesia 1990 and 2010. R Studio/RPubs. Available at https://rpubs.com/quarcs-lab/efficiency-clusters-indonesia-1990-2010

- [Mendez-Guerra, C. (2018). On the distribution dynamics of human development: Evidence from the metropolitan regions of Bolivia''. Economics Bulletin, 38(4), 2467-2475.](http://www.accessecon.com/Pubs/EB/2018/Volume38/EB-18-V38-I4-P223.pdf)


END
